Quantum-Inspired Causal Inference

诚然，仅仅相关性并不意味着因果关系。但是，人们可以通过仔细的假设从统计数据中得出因果结论。因果推理（CI）是一个新兴的数据科学框架，可以做到这一点。请考虑：我们如何才能确定一个广告活动对新产品销售的影响，考虑到不可测量的因素，如内在的愿望？如果我们看到饮食和健康之间的相关性，那么这种饮食是否只是更健康的群体所偏爱的呢？我们如何才能将高等教育对未来财富的影响从能力或机会等因素中分离出来，这些因素也可以解释教育和经济成就？我们能从基因型和表型之间的关联中了解到基因的作用吗？这些问题通过量化变量之间的因果关系的主题统一起来，这些变量之间的因果关系也与隐藏的共同原因有关。这是CI中的一项中心任务，并正式简化为一个低层次的数学问题，涉及表征包含隐变量的不同因果模型的局限性。 同样的低层次问题也出现在量子物理学的研究中，尽管动机并不相关。物理学家关心的是证明他们数据的“量子性”，即，经典解释在（局部）隐变量方面的失败。回顾过去，理论物理学家自1964年以来一直在进行因果推理，尽管现代CI的形式主义直到大约20年后才出现。值得注意的是，这些表面上不相关的学科的交叉点直到最近十年才被加拿大自己的圆周研究所的研究人员所认识。我的研究项目延续了加拿大在因果推理和量子基础（QF）交叉领域的先发优势。这一领域的进展有望通过提高商业数据分析和人工智能的可靠性，以及帮助发现新的量子技术，使加拿大的战略优先事项受益。跨学科的交叉为博士研究提供了独特的机会，既易于处理又有影响力。通常，近期研究目标要么是增量的，要么是高风险的。然而，在这里，博士生几乎可以保证他们的研究的影响。将QF的主要结果翻译为CI就是这样一条途径，因为在经典CI发展中的开创性问题的启发下，量子因果推理中对全新问题的考虑也是如此。除了是跨学科的，这个建议包括基础和转化研究的组成部分。因此，学生将建立一个跟踪记录，有利于在行业和学术界的职业道路。在这些项目中所涉及的分析和计算技能特别便携。学生将通过对自己解决问题的能力和广泛的专业合作获得信心，成长为成熟的科学家。

True, correlation alone does not imply causation. But, one can extract causal conclusions from statistical data with careful assumptions. Causal inference (CI) is the nascent data science framework for doing just that. Consider: How can we determine the impact of an advertising campaign on the sales of a new product, given unmeasurable factors such as innate desirability? If we see correlation between diet and health, could that diet merely be preferred by healthier groups? How can we disentangle the impact of higher education on future wealth from factors such as aptitude or opportunity, which can also explain both educational and economic achievement? What can we learn about the roles of genes from associations between genotypes and phenotypes? These questions are unified by the theme of quantifying the cause-effect relationships between variables which are also related by hidden common causes. This is a central task in CI, and formally reduces to a low-level math problem concerning characterizing the limitations of different causal models involving hidden variables. The same low-level problem turns up in the study of the quantum physics, albeit from unrelated motivations. Physicists care about certifying the "quantumness" of their data, i.e., the failure of classical explanations in terms of (local) hidden variables. In retrospect, theoretical physicists have been doing causal inference since 1964, though the formalism of modern CI didn't emerge until some twenty years later. Significantly, the intersection of these superficially unrelated disciplines was only recognized in the last decade, by researchers at Canada's own Perimeter Institute. My research program continues Canada's first-mover advantage in the intersecting frontiers of causal inference and quantum foundations (QF). Progress in this space promises to benefit Canada's strategic priorities by improving the reliability of commercial data analysis and artificial intelligence, and in aiding the discovery of novel quantum technologies. The interdisciplinary intersection provides unique opportunities for PhD research which is both tractable and impactful. Typically, near-term research targets are either incremental or high risk. Here, however, a PhD student can practically guarantee the impact of their research. The translation of major results for QF to CI is one such avenue, as is the consideration of entirely novel questions in quantum causal inference inspired by seminal questions in the development of classical CI. Aside from being interdisciplinary, this proposal includes both basic and translational research components. Students will therefore establish a track record conducive to career paths in both industry and academia. The analytical and computational skills involved in these projects are especially portable. Students will grow into mature scientists by gaining confidence in their own problem-solving abilities and through extensive professional collaboration.